Is Apply Operations to Maximize Frequency Score easy or hard?

Apply Operations to Maximize Frequency Score is classified as a Hard problem. The challenge lies in recognizing that sorting plus a sliding window can track the cost of aligning elements efficiently. Without this insight, brute force approaches quickly become too slow for large inputs.

Apply Operations to Maximize Frequency Score Python/Java solution

Python and Java implementations typically sort the array and maintain a sliding window while tracking the running sum of elements. The window expands with the right pointer and shrinks when the operation cost exceeds k. This pattern produces a clean O(n log n) solution used in most editorial explanations.

How to solve Apply Operations to Maximize Frequency Score in O(n)?

A pure O(n) solution is not possible because the array must be sorted to reason about increasing elements efficiently. After sorting, a sliding window keeps track of the sum of the current window and calculates the cost needed to match the largest value. This reduces the main computation to O(n) after the O(n log n) sorting step.

What is the best approach for Apply Operations to Maximize Frequency Score?

The most efficient and commonly used solution combines sorting with a sliding window. After sorting the array, expand a two‑pointer window and track the cost required to raise all elements to the rightmost value. If the cost exceeds k, move the left pointer to shrink the window. This approach runs in O(n log n) time due to sorting and O(1) extra space.

Is Apply Operations to Maximize Frequency Score asked at Google/Amazon/Meta?

Problems combining sliding window, prefix sums, and greedy cost calculations frequently appear in interviews at companies like Google, Amazon, and Meta. Variants of this problem test the ability to manage window costs and optimize frequency using limited operations.

What data structure is used in Apply Operations to Maximize Frequency Score?

The main data structures are arrays along with prefix sums for fast range calculations. The optimal approach relies on sorting and a sliding window with two pointers. Some alternative implementations may use priority queues or ordered structures for frequency management.

What is the time complexity of Apply Operations to Maximize Frequency Score?

The optimal solution runs in O(n log n) time. Sorting the array takes O(n log n), and the sliding window traversal is O(n). Alternative solutions using binary search and prefix sums also result in O(n log n) complexity because each feasibility check scans the array.

Description Hints 2 Solution Video 1:06:03

2968. Apply Operations to Maximize Frequency Score

Hard39.3% acceptance3 companies

You are given a 0-indexed integer array nums and an integer k.

You can perform the following operation on the array at most k times:

Choose any index i from the array and increase or decrease nums[i] by 1.

The score of the final array is the frequency of the most frequent element in the array.

Return the maximum score you can achieve.

The frequency of an element is the number of occurences of that element in the array.

Example 1:

Input: nums = [1,2,6,4], k = 3
Output: 3
Explanation: We can do the following operations on the array:
- Choose i = 0, and increase the value of nums[0] by 1. The resulting array is [2,2,6,4].
- Choose i = 3, and decrease the value of nums[3] by 1. The resulting array is [2,2,6,3].
- Choose i = 3, and decrease the value of nums[3] by 1. The resulting array is [2,2,6,2].
The element 2 is the most frequent in the final array so our score is 3.
It can be shown that we cannot achieve a better score.

Example 2:

Input: nums = [1,4,4,2,4], k = 0
Output: 3
Explanation: We cannot apply any operations so our score will be the frequency of the most frequent element in the original array, which is 3.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁹
0 <= k <= 10¹⁴

Asked at 3 companies

Deutsche Bank PhonePe

Google

Topics

Hints open one at a time

Hint 1

If you sort the original array, it is optimal to apply the operations on one subarray such that all the elements of that subarray become equal.

Hint 2

You can use binary search to find the longest subarray where we can make the elements equal in at most k operations.

1:06:03

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